For parts (a) and (b), the determinants must be greater than 0 for the quadratic equations in x to have two real solutions. Therefore, it's a matter of solving the inequalities and .
5a) Find the values of p for which the equation x^2 + px + 8 = p has one positive and one negative root [p > 8]
I have found the determinant to be p^2 + 4p - 32
Please advise how to continue - the answer is not obtained by taking determinant > 0
b) Find the positive value of k for which the equation 6x^2 - 2kx + k = 0 has 2 real roots, one being thrice the other
I have found the determinant to be k^2 - 6k
Please advise how to proceed
c) Given that A and B are the roots of the euqation x^2 = 3x + 5, find the value of 1/A^2 + 1/B^2 and show that A^4 = 57A + 70
I have found the answer to be 19/25, but I've no idea how to show the equation
Please help!
Thanks a lot